Details:
Title  On the complexity of the F5 Gröbner basis algorithm  Author(s)  Magali Bardet, JeanCharles Faugère, Bruno Salvy  Type  Article in Journal  Abstract  We study the complexity of Gröbner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system.
We give a bound on the number of polynomials of degree d in a Gröbner basis computed by Faugère's F5 algorithm (2002) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials for a reduced Gröbner basis, independently of the algorithm used). Next, we analyse more precisely the structure of the polynomials in the Gröbner bases with signatures that F5 computes and use it to bound the complexity of the algorithm.
Our estimates show that the version of F5F5 we analyse, which uses only standard Gaussian elimination techniques, outperforms row reduction of the Macaulay matrix with the best known algorithms for moderate degrees, and even for degrees up to the thousands if Strassen's multiplication is used. The degree being fixed, the factor of improvement grows exponentially with the number of variables.  Keywords  F5 algorithm, Complexity, Regular sequences, Noether position  Length  22  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717114000935 
Language  English  Journal  Journal of Symbolic Computation  Volume  70  Number  0  Pages  4970  Year  2015  Month  September  Translation 
No  Refereed 
No 
